scholarly journals Local Asymptotic Power of Quadratic Rank Tests for Trend

1975 ◽  
Vol 3 (2) ◽  
pp. 401-412 ◽  
Author(s):  
Rudolf Beran
Keyword(s):  
Rank Tests ◽  
Asymptotic Power ◽  
Local Asymptotic Power

ASYMPTOTICALLY UMP PANEL UNIT ROOT TESTS—THE EFFECT OF HETEROGENEITY IN THE ALTERNATIVES

2014 ◽  
Vol 31 (3) ◽  
pp. 539-559 ◽  
Author(s):  
I. Gaia Becheri ◽  
Feike C. Drost ◽  
Ramon van den Akker
Keyword(s):  
Unit Root ◽  
Generalized Least Squares ◽  
Applied Economics ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Optimal Tests ◽  
Independent Panel ◽  
Local Asymptotic Power ◽  
Uniformly Most Powerful

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

THE LOCAL ASYMPTOTIC POWER OF CERTAIN TESTS FOR FRACTIONAL INTEGRATION

1999 ◽  
Vol 15 (5) ◽  
pp. 704-709 ◽  
Author(s):  
Jonathan H. Wright
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Fractional Integration ◽  
Empirical Work ◽  
Local Alternatives ◽  
Asymptotic Power ◽  
Rescaled Range ◽  
Partial Sum Process ◽  
Local Asymptotic Power ◽  
Range Test

It is possible to construct a test of the null of no fractional integration that has nontrivial asymptotic power against a sequence of alternatives specifying that the series is I(d) with d = O(T−1/2), where T is the sample size. In this paper, I show that tests for fractional integration that are based on the partial sum process of the time series have only trivial asymptotic power (i.e., equal to the size) against this sequence of local alternatives. These tests include the rescaled-range test. In this sense, despite its widespread use in empirical work, the rescaled-range test is a poor test for fractional integration.

scholarly journals Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown

1994 ◽  
Vol 10 (3-4) ◽  
pp. 672-700 ◽  
Author(s):  
Graham Elliott ◽  
James H. Stock
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Critical Values ◽  
Asymptotic Power ◽  
Time Series Regression ◽  
Second Stage ◽  
Alternative Approach ◽  
Local Asymptotic Power ◽  
Size Distortions ◽  
Correct Size

The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference—and show that both exhibit substantial size distortions in empirically plausible situations. We then propose an alternative approach in which the second-stage critical values depend continuously on a first-stage statistic that is informative about the order of integration of the regressor. This procedure has the correct size asymptotically and good local asymptotic power.

Combining Alternative Rank Tests for the Multiple Regression Problem

1986 ◽  
Vol 35 (3-4) ◽  
pp. 169-188 ◽  
Author(s):  
Shoutir Kishore Chatterjee ◽  
Tathagata Banerjee
Keyword(s):  
Multiple Regression ◽  
Quadratic Forms ◽  
Null Distribution ◽  
Test Statistic ◽  
Rank Tests ◽  
Asymptotic Power ◽  
Regression Problem ◽  
Test Criterion ◽  
Simultaneous Choice ◽  
Set Up

In this paper we consider the problem of testing absence of regression under the nonparametric multiple regression set up with m predictors. Usual rank tests for this problem are based on particular systems of scores, the test criteria being quadratic forms in m linear rank statistics. Different standard tests correspond to different choices of the system of scores. In this paper we have proposed a test statistic which is based on the simultaneous choice of more than one system of scores. Asymptotic null distribution of the test criterion is a chisquare with m df as in the case of the usual tests. However, the use of several systems of scores results in the improvement of the asymptotic power over the test based on any one of the systems. Ofcourse the use of the test criterion in practice involves the estimation of indices involving the parent density f( . ). Certain standard estimates of these indices are noted in the last section.

scholarly journals A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS

2012 ◽  
Vol 29 (3) ◽  
pp. 609-628 ◽  
Author(s):  
Timothy J. Vogelsang ◽  
Martin Wagner
Keyword(s):  
Unit Root ◽  
Theoretical Explanation ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Long Run ◽  
Local Asymptotic Power ◽  
One Step ◽  
The One

In this paper we extend fixed-b asymptotic theory to the nonparametric Phillips–Perron (PP) unit root tests. We show that the fixed-b limits depend on nuisance parameters in a complicated way. These nonpivotal limits provide an alternative theoretical explanation for the well-known finite-sample problems of the PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step detrending approaches. This is in contrast to the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long-run variance estimator. Based on these results we introduce modified PP tests that allow for asymptotically pivotal fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes, which allows us to study the asymptotic behavior both under the unit root null hypothesis and for local alternatives. The performance of the original and modified PP tests is compared by means of local asymptotic power and a small finite-sample simulation study.

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